and

Square

sSquare

s

Square Roots

Square Roots

We will:• Understand the meaning of squaring a

number and finding the square root of a number

• Find squares of numbers• Raise a whole number to a whole

number power• Find square roots of perfect squares• Find approximate square roots of non-

perfect squares

Shade in graph paper to make each of the shapes below. Each shape is a

square.

Count and write the number of square tiles in each of the larger squares below.1. 2. 3.

Continue to draw larger squares. Make one that is 7 tiles wide and 7 tiles high; then make one that is 8 wide and 8 high. Count the number of squares in each shape.

4. 7 by 7 = ____ 5. 8 by 8 = ____

Talk to the person next to you about the following questions. Be prepared to discuss them if I call on you.

•The numbers 1, 4, 9, 16, 25, etc. are known as perfect squares. Why do you think they are called perfect squares?

•How are the width and the height of the squares related? How are they related to the total number of tiles?

•How could you find the next numbers that are perfect squares without tiles?

If a square measures 4 inches on each side, how would you find its area?

4 inches4

inch

es 4

inch

es

4 inches

Remember how to calculate the area?

4 inches A = l •

w A = 4 in. • 4 in. 4

in

ches

A = 16 in.2

A square must have the same length and

width. 4 inches

A = l • w A = 4 in. • 4 in.

4

inch

es

Square Number• Also called a “perfect square”• A number that is the square

of a whole number• Can be represented by

arranging objects in a square.

Square Numbers

To square a number means to multiply it by

itself.

5 squared means 5 x 5

Take the number 5

And square it!

There is a shorter way to write 5 x 5.

Say:“5 squared” or

“5 to the 2nd power”.

These are the parts.

This is the base

This is the exponent

This is another formula for finding the area of a

square.

sA = s

2

s is the side length

Evaluate it!

B. 49A. 14

Try these:

NumberSquared

Factors StandardForm

92

11119

102

9 9 81112 12132 3 3

10 10

100

These numbers are called perfect squares

If a number is a perfect square, then you can find its exact square root.

A perfect square is simply a number that can be written as the square of another number.

What are the first 10 whole numbers that are perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

2222222222 10,9,8,7,6,5,4,3,2,1

62 = 36 36 = 6

-What’s the opposite operation to addition?

-What’s the opposite operation to multiplication?

-The opposite operation to squaring a number is taking the square root.

The symbol used to indicate a root is the radical symbol -

Every radical expression has three parts…

• Radical symbol• Index• Radicand

Every radical expression has three parts…

Index

Radicand

Radical

2 49

The index of a radical is a whole number greater than or equal to 2.

The index of a square root is always 2.

but is normally written as .

The square root of 49 could be written as …2 49

49

What does square root mean?

The square root of a number is another number which when multiplied by itself gives back the original number.

What is a square root?

the measure of the side of the square

16 = 4

?

What is the square root of 36?

36 =6

49777 2

Example:

because

Also

because

749

749 49777 2

Find the two square roots of each number.

7 is a square root, since 7 • 7 = 49.

–7 is also a square root, since –7 • –7 = 49.

10 is a square root, since 10 • 10 = 100.

–10 is also a square root, since –10 • –10 = 100.

49 = –7–

49 = 7

100 = 10

100 = –10–

A. 49

B. 100

A. 255 is a square root, since 5 • 5 = 25.–5 is also a square root, since –5 • –5 = 25.

12 is a square root, since 12 • 12 = 144.

–12 is also a square root, since –12 • –12 = 144.

25 = –5–25 = 5

144 = 12

144 = –12–

Find the two square roots of each number.

B. 144

Open your books to page 72 so we can try some problems

together